arXiv subjects

Sarp Akcay

Publications and source records attributed to Sarp Akcay.

21 records · Page 2Linked to original sources

arXiv2011

Horizon-absorbed energy flux in circularized, nonspinning black-hole binaries and its effective-one-body representation

We propose, within the effective one body (EOB) approach, a new, resummed, analytical representation of the gravitational wave energy flux absorbed by a system of two circularized (nonspinning) black holes. This expression is such to be well-behaved in the strong-field, fast motion regime, notably up to the EOB-defined last unstable orbit. Building conceptually upon the procedure adopted to resum the multipolar asymptotic energy flux, we introduce a {\it multiplicative} decomposition of the multipolar absorbed flux made by three factors: (i) the leading-order contribution, (ii) an "effective source" and (iii) a new residual amplitude correction $(\tildeρ_\lm^H)^{2\ell}$. In the test-mass limit, we use a frequency-domain perturbative approach to accurately compute numerically the horizon-absorbed fluxes along a sequence of stable and unstable circular orbits and we extract from them the functions $\tildeρ_\lm^H$. These quantities are then fitted via rational functions. The resulting analytically represented test-mass knowledge is then suitably {\it hybridized} with lower-order analytical information that is valid for any mass ratio. This yields a resummed representation of the absorbed flux for a generic, circularized, nonspinning black-hole binary. Our result adds new information to the state-of-the-art calculation of the absorbed flux at fractional 5 post-Newtonian order [S. Taylor and E. Poisson, Phys. Rev. D {\bf 78} 084016 (2008)], that is recovered in the weak-field limit approximation by construction.

gr-qc↗

arXiv2010

Kerr-de Sitter Universe

It is now widely accepted that the universe as we understand it is accelerating in expansion and fits the de Sitter model rather well. As such, a realistic assumption of black holes must place them on a de Sitter background and not Minkowski as is typically done in General Relativity. The most astrophysically relevant black hole is the uncharged, rotating Kerr solution, a member of the more general Kerr-Newman metrics. A generalization of the rotating Kerr black hole to a solution of the Einstein's equation with a cosmological constant $Λ$ was discovered by Carter \cite{DWDW}. It is typically referred to as the Kerr-de Sitter spacetime. Here, we discuss the horizon structure of this spacetime and its dependence on $Λ$. We recall that in a $\La>0$ universe, the term `extremal black hole' refers to a black hole with angular momentum $J > M^2 $. We obtain explicit numerical results for the black hole's maximal spin value and get a distribution of admissible Kerr holes in the ($Λ$, spin) parameter space. We look at the conformal structure of the extended spacetime and the embedding of the 3-geometry of the spatial hypersurfaces. In analogy with Reissner-Nordström -de Sitter spacetime, in particular by considering the Kerr-de Sitter causal structure as a distortion of the Reissner-Nordström-de Sitter one, we show that spatial sections of the extended spacetime are 3-spheres containing 2-dimensional topologically spherical sections of the horizons of Kerr holes at the poles. Depending on how a $t=$ constant 3-space is defined these holes may be seen as black or white holes (four possible combinations).

gr-qc↗

arXiv2009

Area Invariance of Apparent Horizons under Arbitrary Boosts

It is a well known analytic result in general relativity that the 2-dimensional area of the apparent horizon of a black hole remains invariant regardless of the motion of the observer, and in fact is independent of the $ t=constant $ slice, which can be quite arbitrary in general relativity. Nonetheless the explicit computation of horizon area is often substantially more difficult in some frames (complicated by the coordinate form of the metric), than in other frames. Here we give an explicit demonstration for very restricted metric forms of (Schwarzschild and Kerr) vacuum black holes. In the Kerr-Schild coordinate expression for these spacetimes they have an explicit Lorentz-invariant form. We consider {\it boosted} versions with the black hole moving through the coordinate system. Since these are stationary black hole spacetimes, the apparent horizons are two dimensional cross sections of their event horizons, so we compute the areas of apparent horizons in the boosted space with (boosted) $ t = constant $, and obtain the same result as in the unboosted case. Note that while the invariance of area is generic, we deal only with black holes in the Kerr-Schild form, and consider only one particularly simple change of slicing which amounts to a boost. Even with these restrictions we find that the results illuminate the physics of the horizon as a null surface and provide a useful pedagogical tool. As far as we can determine, this is the first explicit calculation of this type demonstrating the area invariance of horizons. Further, these calculations are directly relevant to transformations that arise in computational representation of moving black holes. We present an application of this result to initial data for boosted black holes.

gr-qc↗