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Register a new userPossible Effects of a Cosmological Constant on Black Hole Evolution
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We explore possible effects of vacuum energy on the evolution of black holes. If the universe contains a cosmological constant, and if black holes can absorb energy from the vacuum, then black hole evaporation could be greatly suppressed. For the magnitude of the cosmological constant suggested by current observations, black holes larger than $sim 4 times 10^{24}$ g would accrete energy rather than evaporate. In this scenario, all stellar and supermassive black holes would grow with time until they reach a maximum mass scale of $sim 6 times 10^{55}$ g, comparable to the mass contained within the present day cosmological horizon.
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A scalar field non-minimally coupled to certain geometric [or matter] invariants which are sourced by [electro]vacuum black holes (BHs) may spontaneously grow around the latter, due to a tachyonic instability. This process is expected to lead to a new, dynamically preferred, equilibrium state: a scalarised BH. The most studied geometric [matter] source term for such spontaneous BH scalarisation is the Gauss-Bonnet quadratic curvature [Maxwell invariant]. This phenomenon has been mostly analysed for asymptotically flat spacetimes. Here we consider the impact of a positive cosmological constant, which introduces a cosmological horizon. The cosmological constant does not change the local conditions on the scalar coupling for a tachyonic instability of the scalar-free BHs to emerge. But it leaves a significant imprint on the possible new scalarised BHs. It is shown that no scalarised BH solutions exist, under a smoothness assumption, if the scalar field is confined between the BH and cosmological horizons. Admitting the scalar field can extend beyond the cosmological horizon, we construct new scalarised BHs. These are asymptotically de Sitter in the (matter) Einstein-Maxwell-scalar model, with only mild difference with respect to their asymptotically flat counterparts. But in the (geometric) extended-scalar-tensor-Gauss-Bonnet-scalar model, they have necessarily non-standard asymptotics, as the tachyonic instability dominates in the far field. This interpretation is supported by the analysis of a test tachyon on a de Sitter background.
Virial black-hole mass estimates are presented for 12698 quasars in the redshift interval 0.1<z<2.1, based on modelling of spectra from the Sloan Digital Sky Survey (SDSS) first data release . The black-hole masses of the SDSS quasars are found to lie between $simeq10^{7}Msun$ and an upper limit of $simeq 3times 10^{9}Msun$, entirely consistent with the largest black-hole masses found to date in the local Universe. The estimated Eddington ratios of the broad-line quasars (FWHM geq2000 km s^{-1}) show a clear upper boundary at L_{bol}/L_{Edd}~1, suggesting that the Eddington luminosity is still a relevant physical limit to the accretion rate of luminous broad-line quasars at $zleq 2$. By combining the black-hole mass distribution of the SDSS quasars with the 2dF quasar luminosity function, the number density of active black holes at $zsimeq 2$ is estimated as a function of mass. By comparing the estimated number density of active black holes at $zsimeq 2$ with the local mass density of dormant black holes, we set lower limits on the quasar lifetimes and find that the majority of black holes with mass $geq 10^{8.5}Msun$ are in place by $simeq 2$.
A quantum equation of gravity is proposed using the geometrical quantization of general relativity. The quantum equation for a black hole is solved using the Wentzel-Kramers-Brillouin (WKB) method. Quantum effects of a Schwarzschild black hole are demonstrated by solving the quantum equation while requiring a stationary phase and also by using the Einstein-Brillouin-Keller (EBK) quantization condition, and two approaches shows a consistent result. The WKB method is also applied to the McVittie-Thakurta metric, which describes a system consisting of Schwarzschild black holes and a scalar field. A possible interplay between quantum black holes and a scalar field is investigated in detail. The number density of black holes in the universe is obtained by applying statistical mechanics to a system consisting of black holes and a scalar field. A possible solution to the cosmological constant problem is proposed from a statistical perspective.
We analytically investigate the influence of a cosmic expansion on the shadow of the Schwarzschild black hole. We suppose that the expansion is driven by a cosmological constant only and use the Kottler (or Schwarzschild-deSitter) spacetime as a model for a Schwarzschild black hole embedded in a deSitter universe. We calculate the angular radius of the shadow for an observer who is comoving with the cosmic expansion. It is found that the angular radius of the shadow shrinks to a non-zero finite value if the comoving observer approaches infinity.
We analyze the effect of gravitational radiation reaction on generic orbits around a body with an axisymmetric mass quadrupole moment Q to linear order in Q, to the leading post-Newtonian order, and to linear order in the mass ratio. This system admits three constants of the motion in absence of radiation reaction: energy, angular momentum, and a third constant analogous to the Carter constant. We compute instantaneous and time-averaged rates of change of these three constants. For a point particle orbiting a black hole, Ryan has computed the leading order evolution of the orbits Carter constant, which is linear in the spin. Our result, when combined with an interaction quadratic in the spin (the coupling of the black holes spin to its own radiation reaction field), gives the next to leading order evolution. The effect of the quadrupole, like that of the linear spin term, is to circularize eccentric orbits and to drive the orbital plane towards antialignment with the symmetry axis. In addition we consider a system of two point masses where one body has a single mass multipole or current multipole. To linear order in the mass ratio, to linear order in the multipole, and to the leading post-Newtonian order, we show that there does not exist an analog of the Carter constant for such a system (except for the cases of spin and mass quadrupole). With mild additional assumptions, this result falsifies the conjecture that all vacuum, axisymmetric spacetimes posess a third constant of geodesic motion.
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