# Radiation from a *D*-dimensional collision of shock waves: first order perturbation theory

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## Abstract

We study the spacetime obtained by superimposing two equal Aichelburg-Sexl shock waves in *D* dimensions traveling, head-on, in opposite directions. Considering the collision in a boosted frame, one shock becomes stronger than the other, and a perturbative framework to compute the metric in the future of the collision is setup. The geometry is given, in first order perturbation theory, as an integral solution, in terms of initial data on the null surface where the strong shock has support. We then extract the radiation emitted in the collision by using a D-dimensional generalisation of the Landau-Lifschitz pseudo-tensor and compute the percentage of the initial centre of mass energy *ϵ* emitted as gravitational waves. In *D* = 4 we find *ϵ* = 25*.*0%, in agreement with the result of D’Eath and Payne [12]. As *D* increases, this percentage increases monotonically, reaching 40*.*0% in *D* = 10. Our result is always within the bound obtained from apparent horizons by Penrose, in *D* = 4, yielding 29*.*3%, and Eardley and Giddings [16], in *D* > 4, which also increases monotonically with dimension, reaching 41*.*2% in *D* = 10. We also present the wave forms and provide a physical interpretation for the observed peaks, in terms of the null generators of the shocks.

## Keywords

Large Extra Dimensions Black Holes## References

- [1]N. Arkani-Hamed, S. Dimopoulos and G.R. Dvali,
*The hierarchy problem and new dimensions at a millimeter*,*Phys. Lett.***B 429**(1998) 263 [hep-ph/9803315] [SPIRES].ADSGoogle Scholar - [2]S. Dimopoulos and G.L. Landsberg,
*Black holes at the LHC*,*Phys. Rev. Lett.***87**(2001) 161602 [hep-ph/0106295] [SPIRES].ADSCrossRefGoogle Scholar - [3]S.B. Giddings and S.D. Thomas,
*High energy colliders as black hole factories: the end of short distance physics*,*Phys. Rev.***D 65**(2002) 056010 [hep-ph/0106219] [SPIRES].ADSGoogle Scholar - [4]CMS collaboration, V. Khachatryan et al.,
*Search for microscopic black hole signatures at the Large Hadron Collider*,*Phys. Lett.***B 697**(2011) 434 [arXiv:1012.3375] [SPIRES].ADSGoogle Scholar - [5]The ATLAS collaboration, G. Aad et al.,
*Expected performance of the ATLAS experiment — Detector, trigger and physics*, arXiv:0901.0512 [SPIRES]. - [6]ATLAS Collaboration,
*Search for strong gravity effects in same-sign dimuon final states*, ATLAS-CONF-2011-065, (2011). - [7]ATLAS collaboration,
*Search for microscopic black holes in multi-jet final states with the ATLAS detector at*\( \sqrt {s} = 7 \)*TeV*, ATLAS-CONF-2011-068, (2011). - [8]S.C. Park,
*Critical comment on the recent microscopic black hole search at the LHC*,*Phys. Lett.***B 701**(2011) 587 [arXiv:1104.5129] [SPIRES].ADSGoogle Scholar - [9]J.A. Frost et al.,
*Phenomenology of production and decay of spinning extra-dimensional black holes at hadron colliders*,*JHEP***10**(2009) 014 [arXiv:0904.0979] [SPIRES].ADSCrossRefGoogle Scholar - [10]D.-C. Dai et al.,
*BlackMax: a black-hole event generator with rotation, recoil, split branes and brane tension*,*Phys. Rev.***D 77**(2008) 076007 [arXiv:0711.3012] [SPIRES].ADSGoogle Scholar - [11]G. ’t Hooft,
*Graviton dominance in ultrahigh-energy scattering*,*Phys. Lett.***B 198**(1987) 61 [SPIRES].MathSciNetADSGoogle Scholar - [12]P.D. D’Eath and P.N. Payne,
*Gravitational radiation in high speed black hole collisions.*1*. Perturbation treatment of the axisymmetric speed of light collision*,*Phys. Rev.***D 46**(1992) 658 [SPIRES].MathSciNetADSGoogle Scholar - [13]P.D. D’Eath and P.N. Payne,
*Gravitational radiation in high speed black hole collisions.*2*. Reduction to two independent variables and calculation of the second order news function*,*Phys. Rev.***D 46**(1992) 675 [SPIRES].MathSciNetADSGoogle Scholar - [14]P.D. D’Eath and P.N. Payne,
*Gravitational radiation in high speed black hole collisions.*3*. Results and conclusions*,*Phys. Rev.***D 46**(1992) 694 [SPIRES].MathSciNetADSGoogle Scholar - [15]P.C. Aichelburg and R.U. Sexl,
*On the gravitational field of a massless particle*,*Gen. Rel. Grav.***2**(1971) 303 [SPIRES].ADSCrossRefGoogle Scholar - [16]D.M. Eardley and S.B. Giddings,
*Classical black hole production in high-energy collisions*,*Phys. Rev.***D 66**(2002) 044011 [gr-qc/0201034] [SPIRES].MathSciNetADSCrossRefGoogle Scholar - [17]H. Yoshino and Y. Nambu,
*Black hole formation in the grazing collision of high-energy particles*,*Phys. Rev.***D 67**(2003) 024009 [gr-qc/0209003] [SPIRES].ADSGoogle Scholar - [18]P.D. D’Eath,
*High speed black hole encounters and gravitational radiation*,*Phys. Rev.***D 18**(1978) 990 [SPIRES].MathSciNetADSGoogle Scholar - [19]V.S. Rychkov,
*Black hole production in particle collisions and higher curvature gravity*,*Phys. Rev.***D 70**(2004) 044003 [hep-ph/0401116] [SPIRES].MathSciNetADSGoogle Scholar - [20]H. Yoshino and V.S. Rychkov,
*Improved analysis of black hole formation in high-energy particle collisions*,*Phys. Rev.***D 71**(2005) 104028 [hep-th/0503171] [SPIRES].ADSGoogle Scholar - [21]U. Sperhake, V. Cardoso, F. Pretorius, E. Berti and J.A. Gonzalez,
*The high-energy collision of two black holes*,*Phys. Rev. Lett.***101**(2008) 161101 [arXiv:0806.1738] [SPIRES].ADSCrossRefGoogle Scholar - [22]D.V. Gal’tsov, G. Kofinas, P. Spirin and T.N. Tomaras,
*Transplanckian bremsstrahlung and black hole production*,*Phys. Lett.***B 683**(2010) 331 [arXiv:0908.0675] [SPIRES].ADSGoogle Scholar - [23]Y. Constantinou, D. Gal’tsov, P. Spirin and T.N. Tomaras,
*Scalar bremsstrahlung in gravity-mediated ultrarelativistic collisions*, arXiv:1106.3509 [SPIRES]. - [24]U. Sperhake et al.,
*Cross section, final spin and zoom-whirl behavior in high-energy black hole collisions*,*Phys. Rev. Lett.***103**(2009) 131102 [arXiv:0907.1252] [SPIRES].ADSCrossRefGoogle Scholar - [25]F.R. Tangherlini,
*Schwarzschild field in n dimensions and the dimensionality of space problem*,*Nuovo Cim.***27**(1963) 636 [SPIRES].MathSciNetzbMATHCrossRefGoogle Scholar - [26]H.W. Brinkmann,
*Einstein spaces which are mapped conformally on each other*,*Math. Ann.***18**(1925) 119 [*Proc. Natl. Acad. Sci. U.S.***9**(1923) 1].MathSciNetCrossRefGoogle Scholar - [27]A. Einstein and N. Rosen,
*On gravitational waves*,*J. Franklin Inst.***223**(1927) 43.ADSCrossRefGoogle Scholar - [28]L.D. Landau and E.M. Lifshitz,
*The classical theory of fields*, Course of theoretical physics volume 2, Butterworth Heinemann, U.S.A. (2000).Google Scholar - [29]M. Zilhao et al.,
*Numerical relativity for D dimensional axially symmetric space-times: formalism and code tests*,*Phys. Rev.***D 81**(2010) 084052 [arXiv:1001.2302] [SPIRES].ADSGoogle Scholar - [30]H. Witek et al.,
*Numerical relativity for D dimensional space-times: head-on collisions of black holes and gravitational wave extraction*,*Phys. Rev.***D 82**(2010) 104014 [arXiv:1006.3081] [SPIRES].ADSGoogle Scholar - [31]H. Witek et al.,
*Head-on collisions of unequal mass black holes in D*= 5*dimensions*,*Phys. Rev.***D 83**(2011) 044017 [arXiv:1011.0742] [SPIRES].ADSGoogle Scholar - [32]H. Yoshino and M. Shibata,
*Higher-dimensional numerical relativity: formulation and code tests*,*Phys. Rev.***D 80**(2009) 084025 [arXiv:0907.2760] [SPIRES].MathSciNetADSGoogle Scholar - [33]R. Wald,
*General relativity*, University of Chicago Press, Chicago U.S.A. (1984).zbMATHGoogle Scholar - [34]L. Smarr,
*Gravitational radiation from distant encounters and from headon collisions of black holes: the zero frequency limit*,*Phys. Rev.***D 15**(1977) 2069 [SPIRES].ADSGoogle Scholar - [35]D.V. Galtsov,
*Radiation reaction in various dimensions*,*Phys. Rev.***D 66**(2002) 025016 [hep-th/0112110] [SPIRES].MathSciNetADSGoogle Scholar - [36]V. Cardoso, O.J.C. Dias and J.P.S. Lemos,
*Gravitational radiation in D-dimensional spacetimes*,*Phys. Rev.***D 67**(2003) 064026 [hep-th/0212168] [SPIRES].ADSGoogle Scholar - [37]A.O. Barvinsky and S.N. Solodukhin,
*Echoing the extra dimension*,*Nucl. Phys.***B 675**(2003) 159 [hep-th/0307011] [SPIRES].MathSciNetADSCrossRefGoogle Scholar - [38]D.N. Kabat and M. Ortiz,
*Eikonal quantum gravity and planckian scattering*,*Nucl. Phys.***B 388**(1992) 570 [hep-th/9203082] [SPIRES].ADSCrossRefGoogle Scholar - [39]P. Lodone and V.S. Rychkov,
*Radiation problem in transplanckian scattering*,*JHEP***12**(2009) 036 [arXiv:0909.3519] [SPIRES].ADSCrossRefGoogle Scholar - [40]S.W. Hawking,
*Gravitational radiation from colliding black holes*,*Phys. Rev. Lett.***26**(1971) 1344 [SPIRES].ADSCrossRefGoogle Scholar - [41]E. Berti, V. Cardoso and B. Kipapa,
*Up to eleven: radiation from particles with arbitrary energy falling into higher-dimensional black holes*,*Phys. Rev.***D 83**(2011) 084018 [arXiv:1010.3874] [SPIRES].ADSGoogle Scholar - [42]E. Berti, M. Cavaglia and L. Gualtieri,
*Gravitational energy loss in high energy particle collisions: Ultrarelativistic plunge into a multidimensional black hole*,*Phys. Rev.***D 69**(2004) 124011 [hep-th/0309203] [SPIRES].MathSciNetADSGoogle Scholar - [43]V. Cardoso, E. Berti and M. Cavaglia,
*What we (don’t) know about black hole formation in high-energy collisions*,*Class. Quant. Grav.***22**(2005) L61 [hep-ph/0505125] [SPIRES].MathSciNetADSCrossRefGoogle Scholar - [44]F.G. Friedlander,
*The wave equation on a curved space-time*, Cambridge University Press, Cambridge U.K. (1975).zbMATHGoogle Scholar

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