General Relativity and Quantum Cosmology (gr-qc)

Abstract: In a recent series of papers new exact analytical solutions of Einstein equations representing interior spacetimes sourced by stationary rigidly rotating cylinders of fluids have been displayed. We have first considered a fluid with an axially directed pressure C\'el\'erier, Phys. Rev. D 104, 064040 (2021), J. Math. Phys. 64, 032501 (2023), then a perfect fluid, J. Math. Phys. 64, 022501 (2023), followed by a fluid with an azimuthally directed pressure, J. Math. Phys. 64, 042501 (2023), and finally a fluid where the anisotropic pressure is radially oriented, J. Math. Phys. 64, 052502 (2023). This work is being currently extended to the cases of differentially rotating irrotational fluids. The results are presented in a new series of papers considering, in turn, a perfect fluid source, arXiv:2305.11565 [gr-qc], and the same three anisotropic pressure cases. Here, fluids with an axially directed pressure are considered. A general method for generating new mathematical solutions to the field equations is displayed and three classes are presented so as to exemplify this recipe. Their mathematical and physical properties are analyzed. The first class, named class A, whose other mathematical and physical properties determine a standard configuration, is shown to exhibit a singular axis of symmetry which can be considered as an awkward drawback. The second class, class B, is free from such a singularity but appears to exhibit a negative energy density which characterizes a rather exotic kind of matter. The third class, class C, is the best behaved since it possesses the main properties expected from spacetimes sourced by rather standard fluids. The three classes are matched to an exterior Lewis-Weyl vacuum and the conditions for avoiding an angular deficit are discussed. A comparison with the rigidly rotating fluid case is provided.

Abstract: We explicitly demonstrate that the nonlocal ghost-free ultraviolet modification of general relativity (GR) known as the infinite derivative gravity (IDG) resolves nonscalar curvature singularities in exact solutions of the full theory. We analyze exact pp-wave solutions of GR and IDG describing gravitational waves generated by null radiation. Curvature of GR and IDG solutions with the same energy-momentum tensor is compared in parallel-propagated frames along timelike and null geodesics at finite values of the affine parameter. While the GR pp-wave solution contains a physically problematic nonscalar curvature singularity at the location of the source, the curvature of its IDG counterpart is finite.

Abstract: The ringdown phase of gravitational waves emitted by a perturbed black hole is described by a superposition of exponentially decaying sinusoidal modes, called quasinormal modes (QNMs), whose frequencies depend only on the property of the black hole geometry. The extraction of QNM frequencies of an isolated black hole would allow for testing how well the black hole is described by general relativity. However, astrophysical black holes are not isolated. It remains unclear whether the extra matter surrounding the black holes such as accretion disks would affect the validity of the black hole spectroscopy when the gravitational effects of the disks are taken into account. In this paper, we study the QNMs of a Schwarzschild black hole superposed with a gravitating thin disk. Considering up to the first order of the mass ratio between the disk and the black hole, we find that the existence of the disk would decrease the oscillating frequency and the decay rate. In addition, within the parameter space where the disk model can be regarded as physical, there seems to be a universal relation that the QNM frequencies tend to obey. The relation, if it holds generically, would assist in disentangling the QNM shifts caused by the disk contributions from those induced by other putative effects beyond general relativity. The QNMs in the eikonal limit, as well as their correspondence with bound photon orbits in this model, are briefly discussed.

Abstract: In this paper we study the perturbative regime in the static patch of de Sitter metric in the Regge-Wheeler formalism. After realizing that perturbative regime in a de Sitter spacetime depicted in terms of usual spherical coordinates cannot be extended up to the cosmological horizon, we study perturbative equations, in particular the axial ones, in terms of the tortoise coordinate $r_*$. We show that perturbative regime can be extended up to the cosmological horizon, provided that suitable boundary conditions are chosen. As an application, we explore the Regge-Wheeler equation at short distances by performing a taylor expansion. In order to study some possible quantum effects at short distances, we impose to the equation so obtained the same boundary conditions suitable for a quantum 3D harmonic oscillator. As a result, a discrete spectrum can be obtained. The aforementioned spectrum is analysed and a relation with possible effects denoting quantum behavior of gravitons is suggested.

Abstract: The present paper is devoted to a new black bounce solution that regularize the well-known rotating black string in $3+1$ dimensions. To do so, the procedure pointed out by Simpson-Visser is followed, which has been already applied successfully to other static cases of black strings, with and without electric charge. This method implies to force a bounce on the radial coordinate, such that a wormhole throat arises before the singularity, which renders a regular solution. An analysis of the metric is conducted, showing the interpolation between a regular black hole and a wormhole, what provides a much richer family of solutions than the original metric. Different curvature magnitudes are obtained in order to analyze the regularity of the solution, including the Ricci and Kretschmann scalars. Finally, by following the Einstein field equations the corresponding effective energy-momentum tensor is obtained and the energy conditions are analyzed.

Abstract: We compute the spectrum of linearized gravitational excitations of black holes with substantial angular momentum in the presence of higher-derivative corrections to general relativity. We do so perturbatively to leading order in the higher-derivative couplings and up to order fourteen in the black hole angular momentum. This allows us to accurately predict quasinormal mode frequencies of black holes with spins up to about $70\%$ of the extremal value. For some higher-derivative corrections, we find that sizable rotation enhances the frequency shifts by almost an order of magnitude relative to the static case.

Abstract: Electromagnetic and gravitational perturbations on Kerr spacetime can be reconstructed from solutions to the Teukolsky equations. We study the canonical quantization of solutions to these equations for any integer spin. Our quantization scheme involves the analysis of the Hertz potential and one of the Newman-Penrose scalars, which must be related via the Teukolsky-Starobinsky identities. We show that the canonical commutation relations between the fields can be implemented if and only if the Teukolsky-Starobinsky constants are positive, which is the case both for gravitational perturbations and Maxwell fields. We also obtain the Hadamard parametrix of the Teukolsky equation, which is the basic ingredient for a local and covariant renormalization scheme for non-linear observables. We also discuss the relation of the canonical energy of Teukolsky fields to that of gravitational perturbations.