Thermodynamics Of Ultraspinning Black Holes And Taub-NUT Spacetimes

Studying thermodynamic properties of black holes is one of the most im-portant fundamental subjects in General Relativity（GR）and black hole physics.Recently,a new kind of ultraspinning black hole,which possesses the noncompact horizon topology since its topological sphere has two punctures at the north and south poles,has received an increasing interest.The ultraspinning black hole usu-ally violates the reverse isoperimetric inequality（RII）,and thus is also dubbed the superentropic black hole.In addition,the four-dimensional Lorentzian NUT-charged spacetime being asymptotically locally flat,belongs to a large class of very important exact solutions to Einstein’s field equation in GR.Since the symmet-ric axe of NUT-charged spacetime contains the line/string singularity（commonly referred to as the Misner string）at the north and south poles,this kind of space-time has many very exotic properties.Up to now,the thermodynamic properties of NUT-charged spacetime remain to be unsatisfactory.In this dissertation,we mainly study the ultraspinning black hole,and investigate the thermodynamics of ultraspinning black hole and NUT-charged spacetime.The main results can be summarized as follows:1.We find that the four-dimensional ultraspinning Kerr-Sen-AdS（dyonic）black hole does not always violate the RII.According to the four-dimensional Kerr-Sen-AdS（dyonic）black hole,we obtain their ultraspinning counterpart.We show that this ultraspinning Kerr-Sen-AdS₄（dyonic）black hole does not always violate the reverse isoperimetric inequality（RII）since the value of the isoperimetric ratio can be larger/smaller than,or equal to unity,depending upon where the solution parameters lie in the parameters space.This property is obviously different from that of the ultraspinning Kerr-Newman-AdS₄（dyonic）black hole,which always strictly violates the RII,although both of them have some similar properties in other aspects,such as horizon geometry and conformal boundary.2.We have set up a limit procedure between thermodynamic quantities of ultraspinning black holes and those of their usual rotating AdS counterparts.By deriving a novel Christodoulou-Ruffini-like squared-mass formula for the four-dimensional Kerr-Newman-AdS ultraspinning black hole,we establish a set of very simple relations between thermodynamic quantities of the ultraspinning Kerr-Newman-AdS₄black hole and its usual counterparts.Using these relations,ther-modynamic quantities of the Kerr-Newman-AdS₄ultraspinning black hole can be obtained from those of their usual protypes by taking the ultraspinning limit properly.Then these relations are extended to and shown valid also for the four-dimensional Kerr-Sen-AdS（dyonic）black hole,the singly-rotating Kerr-AdS black holes in all higher dimensions and the double-rotating charged black hole in the five-dimensional minimal gauged supergravity.Thus,it can be inferred that ther-modynamic quantities of all ultraspinning black holes own similar limiting rela-tions to those of their corresponding ordinary rotating AdS black holes,and can be obtained by taking the ultraspinning limit appropriately.3.We have advocated a new idea that “The NUT charge is a thermodynam-ical multi-hair”and put forward a simple,systematic way to study the consistent thermodynamics of all four-dimensional NUT-charged spacetimes.Facilitated by first deriving a new meaningful Christodoulou-Ruffini-type squared-mass formula satisfied by the four-dimensional NUT-charged spacetimes,the consistent ther-modynamic first law and Bekenstein-Smarr mass formulae of these NUT-charged spacetimes are deduced.In this way,the traditional elegant Bekenstein-Hawking one-quarter area-entropy relation can be naturally restored in the Lorentzian and Euclidian sectors of generic NUT-charged spacetime（and all its extensions）with-out imposing any constraint condition.Due to the fact that the NUT charge simultaneously has both rotation-like and electromagnetic charge-like characters,we arrive at a new recognition that it must be a thermodynamical multi-hair;this is not only in sharp contrast with all previous knowledge that it has merely one physical feature,or that it is purely a single solution-parameter,but also the phys-ical meaning of the NUT parameter as a poly-facet can be completely uncovered in the thermodynamical sense.