We construct an analytic model of static semiclassical backreaction for a Schwarzschild black hole in the Hartle–Hawking state enclosed within a finite spherical cavity. Using a minimal renormalized stress–energy tensor consistent with conservation, thermal asymptotics, and horizon regularity, we integrate the reduced semiclassical Einstein equations under Dirichlet boundary conditions at the cavity wall. This yields explicit expressions for the corrections to the mass function, redshift factor, horizon location, and surface gravity. We obtain a closed-form first-order correction to the Hawking temperature in terms of a dimensionless backreaction parameter and the cavity radius. The temperature shift decomposes into redshift renormalization, geometric horizon displacement, and a local energy-density contribution at the horizon. The perturbative expansion is controlled by a parameter of order $$M_P^2/M^2$$ , ensuring validity for macroscopic black holes. The near-horizon geometry retains its universal Rindler $$^{2}\times S^{2}$$ structure, indicating that semiclassical effects renormalize rather than modify the geometric origin of Hawking radiation.

Egypt

G. Nashed

Saudi Arabia

Alnadhief Alfedeel

Romania

Tiberiu Harko

Analytic semiclassical backreaction of a Schwarzschild black hole in a finite cavity: horizon shift, temperature renormalization, and canonical stability in the Hartle–Hawking state

The non-conservation of the energy-momentum tensor in $\textit{f}$($\textit{R}$, $\textit{T}$) gravity can be interpreted as an effective manifestation of dissipation. Motivated by this, we propose a new formulation of $\textit{f}$($\textit{R}$, $\textit{T}$) gravity based on the Herglotz variational principle, which extends the usual Hamilton variational principle to dissipative systems by allowing the Lagrangian to depend explicitly on the action. The resulting gravitational field equations extend those of $\textit{f}$($\textit{R}$, $\textit{T}$) gravity by including Herglotz contributions. In the Newtonian limit, these contributions modify the gravitational potential, allowing us to constrain the Herglotz vector through Mercury’s perihelion precession and the relativistic light deflection. The Herglotz corrections lead to a scaling law consistent with observations from the Cassini spacecraft. Examining two representative cosmological models, the Herglotz vector effectively reduces to a single function that, under suitable conditions, can play the role of a cosmological constant, providing an alternative mechanism for the Universe’s accelerated expansion. Within the Herglotz variational approach, the linear $$f(R,T)=R+\alpha T$$ model, previously ruled out in the standard formulation due to its fixed deceleration parameter, becomes consistent with observations for a certain choice of the Herglotz vector.

Marek Wazny

Lehel Csillag

Portugal

Miguel Pinto

Herglotz-type $\textit{f}$($\textit{R}$, $\textit{T}$) gravity

We investigate the influence of boundary terms in gravitational field theories, by considering that in the Einstein–Hilbert action the boundary can be described by a non-metric Weyl-type geometry. The gravitational action and the the field equations, are thus generalized to include new geometrical terms, coming from the non-metric nature of the boundary, and depending on the Weyl vector, and its covariant derivatives. The field equations obtained within this framework generalize the standard Einstein equations by including in their mathematical structure the Weyl vector, and its covariant derivatives. As an applications of the general formalism we investigate the cosmological evolution in a flat FLRW geometry. We obtain the generalized Friedmann equations, which contain extra terms depending on the Weyl vector and its derivatives, arising due to the presence of the Weylian boundary, and which describe an effective, time dependent dark energy. By imposing to the dark energy an equation of state parameter of the Barboza–Alcaniz type, the Friedmann equations can be solved numerically. We compare the predictions of the Weylian boundary gravitational theory with late-time observational data and the predictions of the $$\Lambda $$ CDM paradigm. Our results show that the Weylian boundary cosmological models give a good description of the observational data, and they can reproduce almost exactly the predictions of the $$\Lambda $$ CDM paradigm. Hence, the extension of gravitational theories through the addition of Weylian boundary terms, in which dark energy has a purely geometric origin, emerges as a viable alternative to standard general relativity.

Iran

Shahab Shahidi

Dark energy and accelerating cosmological evolution in a Universe with a Weylian boundary

Weyl geometric gravity theory, in which gravitational action is constructed from the square of the Weyl curvature scalar and the strength of the Weyl vector, has been intensively investigated recently. The theory admits a scalar–vector–tensor representation, obtained by introducing an auxiliary scalar field, and can therefore be reformulated as a scalar–vector–tensor theory in a Riemann space in the presence of a non-minimal coupling between the Ricci scalar and the scalar field. By assuming that the Weyl vector has only a radial component, an exact spherically symmetric vacuum solution of the field equations can be obtained, depending on three integration constants. As compared to the Schwarzschild solution, the Weyl geometric gravity solution contains two new terms, linear and quadratic, in the radial coordinate, respectively. We consider the possibility of testing and obtaining observational restrictions on the Weyl geometric gravity black hole at the scale of the Solar System, by considering six classical tests of general relativity (gravitational redshift, the Eötvös parameter and the universality of free fall, the Nordtvedt effect, the planetary perihelion precession, the deflection of light by a compact object, and the radar echo delay effect) for an exact spherically symmetric black hole solution of the Weyl geometric gravity. These gravitational effects can be fully explained, and are consistent with the vacuum solution of the Weyl geometric gravity. Moreover, the study of the classical general relativistic tests also allows us to constrain the free parameter of the solution.

Azerbaijan

Mohsen Khodadi

Weyl geometric gravity black holes in light of the Solar System tests

We consider the implications of modified dispersion relations, due to the noncommutativity of spacetime, for a photon gas filling the early Universe in the framework of the Big Bang nucleosynthesis (BBN) processes, during the period of light element formation. We consider three types of deformations present in the dispersion relations for radiation gas, from which we obtain low-temperature corrections to the energy density and pressure. The cosmological implications of the modified equations of state in the BBN era are explored in detail for all radiation models. Effects on the nucleosynthesis process induced by spacetime noncommutativity are investigated by evaluating the abundance of relic nuclei (hydrogen, deuterium, helium-3, helium-4, and lithium-7). Primordial mass fraction estimates and their deviations due to changes in the freezing temperature impose an upper limit on the energy density of deformed photon gas, which follows from the modified Friedmann equations. Deviations from the standard energy density of the radiative plasma are therefore constrained by the abundance of helium-4 nuclei. Upper limits on the free parameters of spacetime noncommutativity are obtained via a numerical analysis performed using the software package. The primordial abundance of light elements is obtained by evaluating thermonuclear reaction rates for the considered noncommutative spacetime models. A Markov chain Monte Carlo (MCMC) analysis allows us to obtain restrictions on the free parameters of the modified dispersion relations. The numerical and statistical approach is implemented in Python code , available on GitHub.

Teodora Matei

Cristian Croitoru

Big Bang Nucleosynthesis constraints on space-time noncommutativity

We investigate the effects that arise from the inclusion of boundary terms in the Einstein gravitational field equations in the Big Bang Nucleosynthesis (BBN) framework. In particular, we consider the possibility that the boundary of the Universe is described by a Weyl type geometry. With the help of the generalized Friedmann equations for a Universe with a Weylian boundary, obtained for a Friedmann–Lemaitre–Robertson–Walker FLRW metric, three distinct cosmological models can be constructed. The cosmological evolution is determined by a dissipative scalar field, and by the Weyl vector coming from the boundary. Several cosmological scenarios are obtained via the appropriate splitting of the generalized energy conservation equation. In the present work we obtain relevant constraints on these models by using the BBN data. In particular, the effects on the BBN that arise in the post warm-inflationary era will be examined by theoretically evaluating the measured abundances of relic nuclei (Hydrogen, Deuterium, Helium-3, Helium-4, and Lithium-7). We consider firstly the primordial mass fraction estimates, and their deviations due to changes in the freezing temperature, which impose an upper limit on the effective energy density obtained from the modified Friedmann equations. The deviation from the standard energy density of the radiative plasma is therefore constrained by the abundances of the Helium-4 nuclei. Secondly, an upper limit will be considered in a numerical analysis performed through the usage of the software package, with the help of which we calculate the primordial abundances of the light elements by evaluating the thermonuclear rates within the considered modified gravity framework. Finally, an MCMC analysis will validate the cosmological model with Weylian boundary contributions, imposing relevant constraints on the initial conditions of the cosmos. The methodology is implemented in the python code , which is available on GitHub.

Big Bang Nucleosynthesis constraints on the cosmological evolution in a Universe with a Weylian boundary

We investigate the properties of compact objects in the f(Q, T) theory, where  $$\mathcal {Q}$$  <math> <mi>Q</mi> </math>   is the non-metricity scalar and  $${ \mathcal {T}}$$  <math> <mi>T</mi> </math>   is the trace of the energy–momentum tensor. We derive an interior analytical solution for anisotropic perfect-fluid spheres in hydrostatic equilibrium using the linear form of  $$f(\mathcal {Q}, { \mathcal {T}})=\mathcal {Q}+\psi { \mathcal {T}}$$  <math> <mrow> <mi>f</mi> <mo>(</mo> <mi>Q</mi> <mo>,</mo> <mi>T</mi> <mo>)</mo> <mo>=</mo> <mi>Q</mi> <mo>+</mo> <mi>ψ</mi> <mi>T</mi> </mrow> </math>  , where  $$\psi $$  <math> <mi>ψ</mi> </math>   represents a dimensional parameter. Based on the observational constraints related to the mass and radius of the pulsar SAX J1748.9-2021,  $$\psi $$  <math> <mi>ψ</mi> </math>   is set to a maximum negative value of  $$\psi _1=\psi / \kappa ^2=-0.04$$  <math> <mrow> <msub> <mi>ψ</mi> <mn>1</mn> </msub> <mo>=</mo> <mi>ψ</mi> <mo>/</mo> <msup> <mi>κ</mi> <mn>2</mn> </msup> <mo>=</mo> <mo>-</mo> <mn>0.04</mn> </mrow> </math>  , where  $$\kappa ^2$$  <math> <msup> <mi>κ</mi> <mn>2</mn> </msup> </math>   is the gravitational coupling constant. The solution results in a stable compact object, which does not violate the speed of sound condition  $$c_s^2\le \frac{c^2}{3}$$  <math> <mrow> <msubsup> <mi>c</mi> <mi>s</mi> <mn>2</mn> </msubsup> <mo>≤</mo> <mfrac> <msup> <mi>c</mi> <mn>2</mn> </msup> <mn>3</mn> </mfrac> </mrow> </math>  . The effective equation of state is similar to the quark matter equation of state, and involves the presence of an effective bag constant. When  $$\psi $$  <math> <mi>ψ</mi> </math>   is negative, the star has a slightly larger size as compared to GR stars with the same mass. The difference in the predicted star size between the theory with a negative  $$\psi $$  <math> <mi>ψ</mi> </math>   and GR for the same mass is attributed to an additional force appearing in the hydrodynamic equilibrium equation. The maximum compactness allowed by the strong energy condition for  $$f(\mathcal {Q}, { \mathcal {T}})$$  <math> <mrow> <mi>f</mi> <mo>(</mo> <mi>Q</mi> <mo>,</mo> <mi>T</mi> <mo>)</mo> </mrow> </math>   theory and for GR is  $$C = 0.514$$  <math> <mrow> <mi>C</mi> <mo>=</mo> <mn>0.514</mn> </mrow> </math>   and 0.419, respectively, with the  $$f(\mathcal {Q}, { \mathcal {T}})$$  <math> <mrow> <mi>f</mi> <mo>(</mo> <mi>Q</mi> <mo>,</mo> <mi>T</mi> <mo>)</mo> </mrow> </math>   prediction about  $$10\%$$  <math> <mrow> <mn>10</mn> <mo>%</mo> </mrow> </math>   higher than the GR one. Assuming a surface density at saturation nuclear density of  $$\rho _{\text {nuc}} = 4\times 10^{14}~\hbox {g}/\hbox {cm}^3$$  <math> <mrow> <msub> <mi>ρ</mi> <mtext>nuc</mtext> </msub> <mo>=</mo> <mn>4</mn> <mo>×</mo> <msup> <mn>10</mn> <mn>14</mn> </msup> <mspace width="3.33333pt"></mspace> <mtext>g</mtext> <mo>/</mo> <msup> <mtext>cm</mtext> <mn>3</mn> </msup> </mrow> </math>  , the maximum mass of the star is  $$4.66 M_\odot $$  <math> <mrow> <mn>4.66</mn> <msub> <mi>M</mi> <mo>⊙</mo> </msub> </mrow> </math>  , with a radius of 14.9 km.

Structure, maximum mass, and stability of compact stars in  $$f(\mathcal {Q,T})$$  <math> <mrow> <mi>f</mi> <mo>(</mo> <mrow> <mi>Q</mi> <mo>,</mo> <mi>T</mi> </mrow> <mo>)</mo> </mrow> </math>   gravity

We consider Klein–Gordon equation in the Dyonic Kerr–Sen black hole background, which is the charged rotating axially symmetric solution of the Einstein–Maxwell–Dilaton–Axion theory of gravity. The black hole incorporates electric, magnetic, dilatonic and axionic charges and is constructed in 3+1 dimensional spacetime. We begin our investigations with the construction of the scalar field’s governing equation, i.e., the covariant Klein–Gordon equation. With the help of the ansatz of separation of variables, we successfully separate the polar part, and find the exact solution in terms of Spheroidal Harmonics, while the radial exact solution is obtained in terms of the Confluent Heun function. The quantization of the quasibound state is done by applying the polynomial condition of the Confluent Heun function that gives rise to discrete complex-valued energy levels for massive scalar fields. The real part is the scalar field relativistic quantized energy, while the imaginary part represents the quasibound states’s decay. We present all of the sixteen possible exact energy solutions for both massive and massless scalars. We also present the investigation the Hawking radiation of the Dyonic Kerr–Sen black hole’s apparent horizon, via the Sigurd–Sannan method by making use of the obtained exact scalar wave functions. The radiation distribution function, and the Hawking temperature are also obtained.

Thailand

David Senjaya

Piyabut Burikham

The exact relativistic scalar quasibound states of the dyonic Kerr–Sen black hole: quantized energy, and Hawking radiation

This article describes the configuration of strange quark stars composed of three flavour quarks in hydrostatic equilibrium considering the energy density profile of Mak and Harko and non-zero strange quark mass ( $$m_s\ne {0}$$  <math> <mrow> <msub> <mi>m</mi> <mi>s</mi> </msub> <mo>≠</mo> <mn>0</mn> </mrow> </math>  ). A suitable stellar model is proposed assuming equation of state of interior matter as modified MIT equation of state in bag model  $$p=\frac{1}{3}(\rho -4B_g)$$  <math> <mrow> <mi>p</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mn>3</mn> </mfrac> <mrow> <mo>(</mo> <mi>ρ</mi> <mo>-</mo> <mn>4</mn> <msub> <mi>B</mi> <mi>g</mi> </msub> <mo>)</mo> </mrow> </mrow> </math>  , where  $$B_g$$  <math> <msub> <mi>B</mi> <mi>g</mi> </msub> </math>   is known as bag constant, to predict the viability of strange stars. The interior of such compact stars is mainly composed of quarks and electrons to establish charge neutrality condition. We have checked the various stability windows depending on the energy per baryon for different values of bag constant  $$B_g$$  <math> <msub> <mi>B</mi> <mi>g</mi> </msub> </math>   and mass of strange quark  $$m_s$$  <math> <msub> <mi>m</mi> <mi>s</mi> </msub> </math>  . We have studied the effect of non-zero mass of the strange quark ( $$m_s$$  <math> <msub> <mi>m</mi> <mi>s</mi> </msub> </math>  ) on the physical properties of the strange star in the context of the modified MIT bag equation of state. We note that the maximum stellar mass decreases with increasing  $$m_s$$  <math> <msub> <mi>m</mi> <mi>s</mi> </msub> </math>  . The model is suitable for predicting the radius, central density and other properties of compact stars having mass  $$\le 2.01M_{\odot }$$  <math> <mrow> <mo>≤</mo> <mn>2.01</mn> <msub> <mi>M</mi> <mo>⊙</mo> </msub> </mrow> </math>  , such as  $$4U~1820-30$$  <math> <mrow> <mn>4</mn> <mi>U</mi> <mspace width="3.33333pt"></mspace> <mn>1820</mn> <mo>-</mo> <mn>30</mn> </mrow> </math>  ,  $$PSR~J1614-2230$$  <math> <mrow> <mi>P</mi> <mi>S</mi> <mi>R</mi> <mspace width="3.33333pt"></mspace> <mi>J</mi> <mn>1614</mn> <mo>-</mo> <mn>2230</mn> </mrow> </math>   etc, which are supposed to be strange stars. The radius of few recently observed compact stars are predicted in our model and they are found to be compatible with the value as predicted from observation. The model is found to be suitable in view of all the necessary criterion along with fulfilment of stability of the stellar configuration as well as stable in view of small radial perturbations.

India

R. Roy

K. Goswami

A. Saha

A. Hakim

P. Chattopadhyay

Stellar model with non-zero strange quark mass ( $$m_s\ne 0$$  <math> <mrow> <msub> <mi>m</mi> <mi>s</mi> </msub> <mo>≠</mo> <mn>0</mn> </mrow> </math>  ) and Mak–Harko density profile admitting observational results

We consider the cosmological implications of the Weyl geometric gravity theory. The basic action of the model is obtained from the simplest conformally invariant gravitational action, constructed, in Weyl geometry, from the square of the Weyl scalar, the strength of the Weyl vector, and a matter term, respectively. The total action is linearized in the Weyl scalar by introducing an auxiliary scalar field. To maintain the conformal invariance of the action the trace condition is imposed on the matter energy–momentum tensor, thus making the matter sector of the action conformally invariant. The field equations are derived by varying the action with respect to the metric tensor, the Weyl vector field, and the scalar field, respectively. We investigate the cosmological implications of the theory, and we obtain first the cosmological evolution equations for a flat, homogeneous and isotropic geometry, described by Friedmann–Lemaitre–Robertson–Walker metric, which generalize the Friedmann equations of standard general relativity. In this context we consider two cosmological models, corresponding to the vacuum state, and to the presence of matter described by a linear barotropic equation of state. In both cases we perform a detailed comparison of the predictions of the theory with the cosmological observational data, and with the standard  $$\Lambda $$  <math> <mi>Λ</mi> </math>   CDM model. By assuming that the presence of the Weyl geometric effects induce small perturbations in the homogeneous and isotropic cosmological background, and that the anisotropy parameter is small, the equations of the cosmological perturbations due to the presence of the Weyl geometric effects are derived. The time evolution of the metric and matter perturbations are explicitly obtained. Therefore, if Weyl geometric effects are present, the Universe would acquire some anisotropic characteristics, and its geometry will deviate from the standard FLRW one.