A Critical Assessment of Black Hole Solutions With a Linear Term in Their Redshift Function

Abstract

Different theories of gravity can admit the same black hole solution, but the parameters usually have different physical interpretations. In this work we study in depth the linear term $\beta r$ in the redshift function of black holes, which arises in conformal gravity, de Rham-Gabadadze-Tolley (dRGT) massive gravity, $f(R)$ gravity (as approximate solution) and general relativity. Geometrically we quantify the parameter $\beta$ in terms of the curvature invariants. Astrophysically we found that $\beta$ can be expressed in terms of the cosmological constant, the photon orbit radius and the innermost stable circular orbit (ISCO) radius. The metric degeneracy can be broken once black hole thermodynamics is taken into account. Notably, we show that under Hawking evaporation, different physical theories with the same black hole solution (at the level of the metric) can lead to black hole remnants with different values of their physical masses with direct consequences on their viability as dark matter candidates. In particular, the mass of the graviton in massive gravity can be expressed in terms of the cosmological constant and of the formation epoch of the remnant. Furthermore the upper bound of remnant mass can be estimated to be around $0.5\times 10^{27}$ kg.

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References in corpus (79)

• f(R) Theories Of Gravity
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• f(R) theories
• Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
• Resummation of Massive Gravity
• Evolution of Binary Black Hole Spacetimes
• Accurate Evolutions of Orbiting Black-Hole Binaries Without Excision
• Gravitational wave extraction from an inspiraling configuration of merging black holes
• Theoretical Aspects of Massive Gravity
• Quintessence and black holes
• Primordial Black Holes - Perspectives in Gravitational Wave Astronomy -
• Shadows of Kerr black holes with scalar hair
• One-loop f(R) gravity in de Sitter universe
• Modified gravity with $\ln R$ terms and cosmic acceleration
• Photon Regions and Shadows of Kerr-Newman-NUT Black Holes with a Cosmological Constant
• Influence of a plasma on the shadow of a spherically symmetric black hole
• Friedmann Equations of FRW Universe in Scalar-tensor Gravity, f(R) Gravity and First Law of Thermodynamics
• Shadow of a black hole surrounded by dark matter
• Shadow of a rotating braneworld black hole
• Black Hole Relics and Inflation: Limits on Blue Perturbation Spectra
• The Current Ability to Test Theories of Gravity with Black Hole Shadows
• Dark Energy: the equation of state description versus scalar-tensor or modified gravity
• Black hole shadow in an asymptotically-flat, stationary, and axisymmetric spacetime: The Kerr-Newman and rotating regular black holes
• No observational proof of the black-hole event-horizon
• Shadows of Einstein-dilaton-Gauss-Bonnet black holes
• Entropy and universality of Cardy-Verlinde formula in dark energy universe
• Friedmann Equations and Thermodynamics of Apparent Horizons
• Black hole shadow in an expanding universe with a cosmological constant
• Constraining the spin and the deformation parameters from the black hole shadow
• Black Hole Remnants and Dark Matter
• Influence of quintessence dark energy on the shadow of black hole
• Schwarzschild black hole surrounded by quintessence: Null geodesics
• Impact of a global quadratic potential on galactic rotation curves
• Melanopogenesis: Dark Matter of (almost) any Mass and Baryonic Matter from the Evaporation of Primordial Black Holes weighing a Ton (or less)
• Critical phenomena of static charged AdS black holes in conformal gravity
• Wald's entropy is equal to a quarter of the horizon area in units of the effective gravitational coupling
• The Kiselev black hole is neither perfect fluid, nor is it quintessence
• Dynamics of test particles around a Bardeen black hole surrounded by perfect fluid dark matter
• Astrophysical imaging of Kerr black holes with scalar hair
• Physical observability of horizons
• Strong Gravitational Lensing by Kiselev Black Hole
• f(R) Gravity: From the Pioneer Anomaly to the Cosmic Acceleration
• Topological Black Holes in Weyl Conformal Gravity
• Geodesic Motion in Schwarzschild Spacetime Surrounded by Quintessence
• Can the dynamics of test particles around charged stringy black holes mimic the spin of Kerr black holes?
• Shadows of CPR black holes and tests of the Kerr metric
• Analytical solutions of the geodesic equation in the spacetime of a black hole in f(R) gravity
• Thermodynamic geometry of black holes in f(R) gravity
• Invariant characterization of the Kerr spacetime: Locating the horizon and measuring the mass and spin of rotating black holes using curvature invariants
• Fitting rotation curve of galaxies by de Rham-Gabadadze-Tolley massive gravity
• Local Invariants Vanishing on Stationary Horizons: A Diagnostic for Locating Black Holes
• The mass of the graviton and the cosmological constant
• Dynamics of charged particles and magnetic dipoles around magnetized quasi-Schwarzschild black holes
• Geometric Horizons
• Identification of black hole horizons using scalar curvature invariants
• Curvature Invariants and Lower Dimensional Black Hole Horizons
• Marginally Stable Circular Orbits in Schwarzschild Black Hole Surrounded by Quintessence Matter
• Scalar Polynomial Curvature Invariant Vanishing on the Event Horizon of Any Black Hole Metric Conformal to a Static Spherical Metric
• Black hole evaporation in Conformal (Weyl) gravity
• Stability and Quasinormal Modes of Black Holes in Conformal Weyl Gravity
• Lyapunov exponent ISCO and Kolmogorov Senai entropy for Kerr Kiselev black hole
• Hawking Evaporation of Black Holes in Massive Gravity
• Black Hole Remnant in Massive Gravity
• Motion of spinning particles in non asymptotically flat spacetimes
• Quasinormal modes of black holes in Weyl gravity: Electromagnetic and gravitational perturbations
• Analytic solutions of the geodesic equation for Reissner-Nordström-(anti-)de Sitter black holes surrounded by different kinds of regular and exotic matter fields
• Black hole solutions correspondence between conformal and massive theories of gravity
• Comment on "Impact of a Global Quadratic Potential on Galactic Rotation Curves"
• Quasilocal energy in modified gravity
• Motion of massive particles around a charged Weyl black hole and the geodetic precession of orbiting gyroscopes
• Quasi-normal Modes of near-extremal black holes in Generalized spherically symmetric spacetime and Strong Cosmic Censorship Conjecture
• Accretion disks around a static black hole in $f(R)$ gravity
• Geometric Horizons in the Kastor-Traschen Multi Black Hole Solutions
• Gravitomagnetic effects in conformal gravity
• Event Horizon Detecting Invariants
• Bending of light in the Universe filled with quintessential dark energy
• A family of solutions to the inverse problem in gravitation: building a theory around a metric
• Quasilocal mass in scalar-tensor gravity: spherical symmetry
• On the Curvature Invariants of the Massive Banados-Teitelboim-Zanelli Black Holes and Their Holographic Pictures

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