Behaviour of matter close to the event horizon

ABSTRACT Investigation of the behaviour of accreting matter close to the black hole event horizonis of fundamental importance in relativistic and high energy astrophysics because theyprovide the key features of the diagnostic spectra of the stellar mass and super-massiveblack holes. In this paper, we examine the terminal behaviour of general relativis-tic matter in multi-transonic, advective black hole accretion discs. We compute, forthe ﬁrst time we believe, the values of various dynamical and thermodynamic multi-transonic ﬂow variables extremely close (≤0.01 r g ) to the event horizon and study thedependence of these variables on fundamental accretion parameters. Our calculationis useful for a better understanding of Hawking radiation from acoustic black holes.Key words: Accretion, accretion discs — black hole physics — general relativity —hydrodynamics — Hawking Radiation 1 INTRODUCTIONGravitational capture of surrounding ﬂuid by massive astrophysical objects is known as accretion. There remains a major dif-ference between black hole (BH) accretion and accretion onto other cosmic objects including neutron stars and white dwarfs.For celestial bodies other than black holes, infall of matter terminates either by a direct collision with the hard surface of theaccretor or with the outer boundary of the magneto-sphere, resulting the luminosity through energy release from the surface.Whereas for black hole accretion, matter ultimately dives through the event horizon from where radiation is prohibited toescape according to the rule of classical general relativity (GR) and the emergence of luminosity occurs on the way towardsthe black hole event horizon. The eﬃciency of accretion process may be thought as a measure of the fractional conversion ofgravitational binding energy of matter to the emergent radiation and is considerably high for black hole accretion comparedto accretion onto any other astrophysical objects. Hence accretion onto classical astrophysical black holes has been recognizedas a fundamental phenomena of increasing importance in relativistic and high energy astrophysics (Frank, King & Raine1992, hereafter FKR, Shapiro & Teukolsky 1983). The extraction of gravitational energy from the black hole accretion isbelieved to power the energy generation mechanism of X-ray binaries and of the most luminous objects of the Universe, theQuasars and active galactic nuclei (AGN). The BH accretion is, thus, the most appealing way through which the all pervadingpower of gravity is explicitly manifested. If the infalling matter does not possess intrinsic angular momentum, accretion ﬂowremains spherically symmetric. However, Inter stellar / intergalactic ﬂuid is always likely to posses non-vanishing rotationalenergy, suﬃcient to dynamically break the spherical symmetry, and in almost all real physical situations, accreting matter isthrown into circular orbits around the central accretor, leading to the formation of the accretion disc around the galactic andextra-galactic black holes.If the instantaneous dynamical velocity and local acoustic velocity of the accreting ﬂuid, moving along a space curve parame-terized by r, are u(r) and a(r) respectively, then the local Mach number M(r) of the ﬂuid can be deﬁned as M(r) =