Self-Gravitating Matter in Stationary and Axisymmetric Black Hole Spacetimes

Abstract

All black holes (BHs) in nature are expected to be described by the Kerr vacuum solution of general relativity (GR). However, the Kerr BH interior contains several problematic features such as a Cauchy horizon, a curvature singularity, and a causality-violating region. Non-Kerr BH models, which are used to examine the genericity of these features, typically contain nontrivial matter content. When such matter is minimally-coupled to Einstein-Hilbert gravity, the Einstein equations can be directly used to investigate its physical properties. We examine properties of the matter in a broad class of stationary and axisymmetric, geodesically-integrable BH spacetimes, and how they are linked to features of the spacetime geometry. In these spacetimes, we find the matter to typically flow along timelike Killing orbits in the BH exterior, usually exhibiting differential rotation but sometimes additionally also non-rigid rotation. At a horizon, the matter rest-frame energy density, $\epsilon$, and principal normal pressure, $p_n$, are shown to necessarily satisfy $p_n=-\epsilon$, implying that only specific types of matter can thread stationary event horizons (e.g., electromagnetic fields but not massless real scalar fields). Furthermore, we show the matter to be comoving with the interior cosmology. We also obtain simple expressions for the expansions of the ingoing and outgoing zero angular momentum null congruences and comment on the light-focussing behavior of the cosmology. Finally, we verify above results explicitly by working with a representative set of well-known BH spacetimes which contain various types of matter -- scalar fields, electromagnetic fields, anisotropic fluids. Some spacetimes have singularities while others have regular interiors. In the exterior, the matter satisfies the weak energy condition. The framework developed here can be extended to cover more general spacetimes.

20 pages + appendices, 7 figures, 2 tables. Shortened version with improved discussion, results unchanged

References in corpus (45)

• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• First Sagittarius A* Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole in the Center of the Milky Way
• First M87 Event Horizon Telescope Results. VI. The Shadow and Mass of the Central Black Hole
• Tests of General Relativity with Binary Black Holes from the second LIGO-Virgo Gravitational-Wave Transient Catalog
• Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A${}^{\ast }$
• First Sagittarius A* Event Horizon Telescope Results. VI: Testing the Black Hole Metric
• Rotating regular black holes
• Generating rotating regular black hole solutions without complexification
• Notes on non-singular models of black holes
• Constraints on black-hole charges with the 2017 EHT observations of M87*
• Gravitational Test Beyond the First Post-Newtonian Order with the Shadow of the M87 Black Hole
• The Shape of the Black Hole Photon Ring: A Precise Test of Strong-Field General Relativity
• New parametrization for spherically symmetric black holes in metric theories of gravity
• Novel black-bounce spacetimes: wormholes, regularity, energy conditions, and causal structure
• Shadow and Quasinormal Modes of a Rotating Loop Quantum Black Hole
• Non-radial oscillations of anisotropic neutron stars in the Cowling approximation
• Black hole shadow in a general rotating spacetime obtained through Newman-Janis algorithm
• Shadow cast and deflection of light by charged rotating regular black holes
• Bumpy Black Holes in Alternate Theories of Gravity
• A novel family of rotating black hole mimickers
• Hidden symmetries, null geodesics, and photon capture in the Sen black hole
• Gravitational decoupling for axially symmetric systems and rotating black holes
• Field sources for Simpson-Visser space-times
• Quasinormal modes, quasiperiodic oscillations and shadow of rotating regular black holes in non-minimally coupled Einstein-Yang-Mills theory
• Key Science Goals for the Next-Generation Event Horizon Telescope
• When is g_{tt} g_{rr} = -1?
• Asymptotic safety casts its shadow
• Achronal averaged null energy condition
• Testing Rotating Regular Metrics with EHT Results of Sgr A*
• Interior of a Schwarzschild black hole revisited
• Spinning Loop Black Holes
• Janis-Newman algorithm: generating rotating and NUT charged black holes
• The Black Hole Explorer: Motivation and Vision
• Self-Similar Force-Free Wind From an Accretion Disk
• Reference Array and Design Consideration for the next-generation Event Horizon Telescope
• Geodesic incompleteness of some popular regular black holes
• Accurate mapping of spherically symmetric black holes in a parameterised framework
• Quantum rotating black holes
• Spinning black holes with a separable Hamilton-Jacobi equation from a modified Newman-Janis algorithm
• Probing spacetime and accretion model for the Galactic Center: Comparison of Kerr and dilaton black hole shadows
• Signatures of regular black holes from the shadow of Sgr A* and M87*
• An extension of the Newman-Janis algorithm
• Testing black hole equatorial reflection symmetry using Sgr A* shadow images
• Toward General-Relativistic Magnetohydrodynamics Simulations in Stationary Non-Vacuum Spacetimes
• On the Possible Spacetime Structures of Rotating Loop Quantum Black Holes

Cited by in corpus (3)

• Two descriptions of dark matter around a black hole: photon sphere, shadow, and lensing
• Geometric properties of slowly rotating black holes embedded in matter environments
• Observational distinguishability of the Kerr and Kerr-Hayward metrics to EHT