Buchdahl star is the most compact object without an event horizon and is an excellent candidate for a black hole mimicker. Unlike black holes, rotating Buchdahl star can be over-extremal with respect to the black hole, sustaining a larger spin. We show that it can also develop an ergosphere above the threshold spin  $$\beta &gt; 1/\sqrt{2}$$  <math> <mrow> <mi>β</mi> <mo>&gt;</mo> <mn>1</mn> <mo>/</mo> <msqrt> <mn>2</mn> </msqrt> </mrow> </math>  , which allows extraction of its rotational energy. Electromagnetic field around Buchdahl star is also expected to differ from that of black hole in both strength and topology. In this paper, we explore the energetics of Buchdahl star focusing on the magnetic Penrose process in the two magnetic field configurations, i.e., uniform and dipole. Below the threshold spin, Buchdahl star is expected to be quiet, while above the threshold it can be much more efficient than the black hole if a dipolar magnetic field is developed on its surface.

China

Uzbekistan

Azerbaijan

Sanjar Shaymatov

South Africa

India

Naresh Dadhich

Czechia

Germany

Arman Tursunov

Energetics of Buchdahl stars and the magnetic Penrose process

It was shown long back in [1] that a non-extremal black hole cannot be converted into an extremal one by test particle adiabatic accretion. The Buchdahl star is the most compact object without horizon and is defined by <math><mi>Φ</mi><mo>(</mo><mi>R</mi><mo>)</mo><mo>=</mo><mn>4</mn><mo>/</mo><mn>9</mn></math>, while black hole by <math><mi>Φ</mi><mo>(</mo><mi>R</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>/</mo><mn>2</mn></math>. Here <math><mi>Φ</mi><mo>(</mo><mi>R</mi><mo>)</mo></math> is the gravitational potential experienced by a particle, radially falling for static and axially for the rotating object. In this short note we examine the question of extremalization of the Buchdhal star and show that the same result holds good as for the black hole. That is, a non-extremal Buchdahl star cannot be extremalized by test particle accretion. Further since extremal limit for BS is &gt;1, it could facilitate formation of extremal black holes by neutral and spinless accretion. That is perhaps the only way they could be formed.

Like black holes, Buchdahl stars cannot be extremalized

Buchdahl sphere, the limiting stable isotropic stellar structure without exotic matter, plays a very important role in our understanding of how compact an astrophysical object can be. Here, we show certain universal properties associated with the Buchdahl sphere, in the sense that these properties will not change with the inclusion of electric charge in the stellar structure, or, will hold good in the pure Lovelock theories of gravity as well. Using these universalities, we have proposed a Buchdahl limit for a slowly-rotating stellar configuration, for the first time. Finally, the universality of the Buchdahl sphere in terms of the gravitational and non-gravitational field energies, as well as for the photon sphere have also been discussed.

Sumanta Chakraborty

Universality of the Buchdahl sphere

The strong cosmic censorship conjecture, whose validation asserts the deterministic nature of general relativity, has been studied for charged BTZ black holes in three dimensional general relativity, as well as for Nth order pure Lovelock gravity in d=2N+1 spacetime dimensions. Through both analytical and numerical routes, we have computed the ratio of the imaginary part of the quasi-normal mode frequencies with the surface gravity at the Cauchy horizon. The lowest of which corresponds to the key parameter associated with violation of strong cosmic censorship conjecture. Our results demonstrate that this parameter is always less than the critical value (1/2), thereby respecting the strong cosmic censorship conjecture. This is in complete contrast to the four or, higher dimensional black holes, as well as for rotating BTZ black hole, where the violation of strong cosmic censorship conjecture exists. Implications and possible connection with the stability of the photon orbits have been discussed.

Chiranjeeb Singha

Strong cosmic censorship conjecture for a charged BTZ black hole

We obtain an exact  $$\Lambda $$  <math> <mi>Λ</mi> </math>  -vacuum solution in the pure Gauss–Bonnet gravity with NUT charge in six dimension, with horizon having the product topology of  $$S^{(2)} \times S^{(2)}$$  <math> <mrow> <msup> <mi>S</mi> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </msup> <mo>×</mo> <msup> <mi>S</mi> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </msup> </mrow> </math>  . We discuss its horizon and singularity structure, and consequently arrive at parameter windows for its physical viability. It turns out that for the curvatures to remain function of r alone for NUT black hole spacetime, horizon topology has to be product of  $$S^{(2)}$$  <math> <msup> <mi>S</mi> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </msup> </math>   spheres. This is true for Einstein as well as for pure Gauss–Bonnet gravity, and perhaps would hold good for higher order pure Lovelock as well.

Sajal Mukherjee

Pure Gauss–Bonnet NUT black hole solution: I

It is known that NUT solution has many interesting features and pathologies like being non-singular and having closed timelike curves. It turns out that in higher dimensions horizon topology cannot be spherical but it has instead to be product of 2-spheres so as to retain radial symmetry of spacetime. In this letter we wish to present a new solution of pure Gauss–Bonnet  $$\Lambda $$  <math> <mi>Λ</mi> </math>  -vacuum equation describing a black hole with NUT charge. It has three interesting cases: (a) black hole with both event and cosmological horizons with singularity being hidden behind the former, (b) a regular spacetime free of both horizon and singularity, and (c) black hole with event horizon without singularity and cosmological horizon. Singularity here is always non-centric at  $$r \ne 0$$  <math> <mrow> <mi>r</mi> <mo>≠</mo> <mn>0</mn> </mrow> </math>  .

Pure Gauss–Bonnet NUT black hole with and without non-central singularity

We wish to construct a model for charged star as a generalization of the uniform density Schwarzschild interior solution. We employ the Vaidya and Tikekar ansatz (Astrophys Astron 3:325, 1982) for one of the metric potentials and electric field is chosen in such a way that when it is switched off the metric reduces to the Schwarzschild. This relates charge distribution to the Vaidya–Tikekar parameter, k, indicating deviation from sphericity of three dimensional space when embedded into four dimensional Euclidean space. The model is examined against all the physical conditions required for a relativistic charged fluid sphere as an interior to a charged star. We also obtain and discuss charged analogue of the Buchdahl compactness bound.

Ranjan Sharma

Shyam Das

Sunil Maharaj

An electromagnetic extension of the Schwarzschild interior solution and the corresponding Buchdahl limit

The recently proposed effective equation of motion for the 4D-Einstein–Gauss–Bonnet gravity admits a static black hole solution that has, like the Rissner–Nordström charged black hole, two horizons instead of one for the Schwarzschild black hole. This means that the central singularity is timelike instead of spacelike. It should though be noted that in  $$D\ge 5$$  <math> <mrow> <mi>D</mi> <mo>≥</mo> <mn>5</mn> </mrow> </math>  , the solution always admits only one horizon like the Schwarzshild solution. In the equation defining the horizon, the rescaled Gauss–Bonnet coupling constant appears as a new ‘gravitational charge’ with a repulsive effect to cause in addition to event horizon a Cauchy horizon. Thus it radically alters the causal structure of the black hole.

On causal structure of 4D-Einstein–Gauss–Bonnet black hole

Generally a black hole could be over-charged/spun, violating the weak cosmic censorship conjecture (WCCC) for linear order accretion while the same is always restored for non-linear accretion. The only exception, however, is that of a five-dimensional rotating black hole with single rotation, which cannot be overspun even at linear order. In this paper we investigate this question for a five-dimensional charged rotating minimally gauged supergravity black hole and show that it could not be overspun under non-linear accretion, thereby respecting WCCC. However, in the case of single rotation WCCC is also respected for linear accretion when the angular momentum of the accreting particle is greater than its charge irrespective of the relative dominance of the charge and rotation parameters of the black hole.

Bobomurat Ahmedov

Pakistan

Mubasher Jamil

Five-dimensional charged rotating minimally gauged supergravity black hole cannot be over-spun and/or over-charged in non-linear accretion

Even though the Myers–Perry five dimensional rotating black hole with two rotations could be overspun by test particle accretion, yet it turns out as we show in this letter that it cannot do so for a single rotation. On the other hand it is known that there exists no extremal limit for a black hole with single rotation in dimensions greater than equal to six. It has been proven that all higher dimensional ($$&gt;4$$ <math><mrow><mo>&gt;</mo><mn>4</mn></mrow></math> ) rotating black holes with only one single rotation can never be overspun under test particle linear accretion and hence would always obey CCC in the weak form.