We examine a loop quantum gravity (LQG) inspired rotating black hole, treating it as a central supermassive black hole (SMBH) in an extreme mass-ratio inspiral (EMRI) system, where an inspiralling object exhibits eccentric motion around the SMBH. With the orbital dynamics, we derive analytical expressions for the rate of change of orbital energy and angular momentum, as well as orbital evolution, and subsequently generate the gravitational waveforms. To evaluate the difference between EMRI waveforms emitted from the Kerr black hole and a spinning black hole in LQG, we compute the dephasing and mismatch using the Laser Interferometer Space Antenna (LISA) observation. Our result indicates that LISA can distinguish the modified effect of LQG with a parameter as small as $$2\times 10^{-6}$$ . The constraint on a parameter in LQG using the Fisher information matrix can be obtained within a fraction error of $$10^{-6}$$ .

China

Tieguang Zi

India

Shailesh Kumar

Eccentric extreme mass-ratio inspirals: a gateway to probe quantum gravity effects

In this paper, we calculated the extreme mass-ratio inspiral (EMRI) waveform radiated from a binary composed of a massive horizonless object (MHO) and a compact object (CO), where CO is spiraling on a circular equatorial orbit around the MHO. Due to the absent of horizon, there exist the ingoing and outgoing waves near the reflective surface of MHO, which have significantly influence on the evolution of orbital parameters. We observe that there indeed exist the differences of EMRI trajectories between the massive Kerr black hole and MHO cases. By calculating the mismatch of gravitational wave (GW) waveforms from massive black hole (MBH) and MHO, our result indicates that the space-borne gravitational wave detector could distinguish the modified effect of reflectivities from the BH case, which allows to put an upper constraint on the reflectivity  $${\mathcal {R}}$$  <math> <mi>R</mi> </math>   of MHO, at the level of  $${\mathcal {R}} &gt; rsim 10^{-4}$$  <math> <mrow> <mi>R</mi> <mo>≳</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>4</mn> </mrow> </msup> </mrow> </math>  .

Liangliang Ren

Jun Cheng

Extreme mass-ratio inspiral around the horizonless massive object

Extreme mass-ratio inspiral (EMRI), as one of most important and promising gravitational wave (GW) sources, which is the ideal tool to test fundamental theories and nature of massive black hole (MBH). In this paper, we consider the EMRI system consisting of a rotating barneworld MBH with tidal charge Q and a stellar-mass compact object (CO), where a non-spinning CO inspirals on the equatorial and circular orbits around the MBH. Under the adiabatic approximate condition, we show the evolution of circular orbital radius by computing the EMRI fluxes and orbital phase modified by tidal charge. We find that the positive and negative values of tidal charges have the difference influences on the EMRI orbital dynamics. In particular, the inspiral motion of CO in the rotating barneworld MBH with a negative tidal charge would be end more earlier than the positive tidal charge case. Accordingly, the EMRI waveforms from the positive tidal charge cases can put more rigorous constraint results comparing with the negative tidal charge cases. Finally, we analyze the phase differences of two EMRI waveforms from Kerr BH and rotating braneworld BH with tidal charge by computing dephasing and mismatch. Our results indicate that LISA can distinguish the EMRI waveforms from rotating braneworld BH with the negative tidal charge as small as <math><msub><mrow><mi>Q</mi></mrow><mrow><mi>min</mi></mrow></msub><mo>∼</mo><mo>−</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>6</mn></mrow></msup></math> under the suitable scenarios, which can sever as the unique discriminator of detecting the physics of extra dimensions.

Extreme mass-ratio inspiral as a probe of extra dimensions: The case of spinning massive object

We study the holographic s+p insulator/superconductor phase transition at zero temperature by using the model with a scalar triplet charged under an SU(2) gauge field in anti-de Sitter (AdS) soliton background. In this model, besides the insulator phase, s-wave condensate phase and p-wave condensate phase, the s+p coexisting condensate phase is found numerically when operator dimension Δ is greater than a critical value Δc . We also construct the complete phase diagram in Δ−μ plane, which shows the s+p coexisting region is very narrow. Furthermore, we calculate the corresponding conductivities for different phases. The delta function support for the real part of conductivity of the spontaneous breaking phases is also revealed numerically as expected for the superconducting phases.