616 research outputs found

    A skeleton approximate solution of the Einstein field equations for multiple black-hole systems

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    An approximate analytical and non-linear solution of the Einstein field equations is derived for a system of multiple non-rotating black holes. The associated space-time has the same asymptotic structure as the Brill-Lindquist initial data solution for multiple black holes. The system admits an Arnowitt-Deser-Misner (ADM) Hamiltonian that can particularly evolve the Brill-Lindquist solution over finite time intervals. The gravitational field of this model may properly be referred to as a skeleton approximate solution of the Einstein field equations. The approximation is based on a conformally flat truncation, which excludes gravitational radiation, as well as a removal of some additional gravitational field energy. After these two simplifications, only source terms proportional to Dirac delta distributions remain in the constraint equations. The skeleton Hamiltonian is exact in the test-body limit, it leads to the Einsteinian dynamics up to the first post-Newtonian approximation, and in the time-symmetric limit it gives the energy of the Brill-Lindquist solution exactly. The skeleton model for binary systems may be regarded as a kind of analytical counterpart to the numerical treatment of orbiting Misner-Lindquist binary black holes proposed by Gourgoulhon, Grandclement, and Bonazzola, even if they actually treat the corotating case. Along circular orbits, the two-black-hole skeleton solution is quasi-stationary and it fulfills the important property of equality of Komar and ADM masses. Explicit calculations for the determination of the last stable circular orbit of the binary system are performed up to the tenth post-Newtonian order within the skeleton model.Comment: 15 pages, 1 figure, submitted to Phys. Rev. D, 3 references added, minor correction

    The anti-NGF antibody muMab 911 both prevents and reverses pain behaviour and subchondral osteoclast numbers in a rat model of osteoarthritis pain

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    Objective: Nerve growth factor (NGF) has a pivotal role in peripheral hyperalgesia and inflammation; anti-NGF antibodies attenuate pain responses in inflammatory pain models, and in people with osteoarthritis (OA) or low back pain. The aim of this study was to characterise the peripheral mechanisms contributing to the analgesic effects of anti-NGF antibody treatment in an established model of joint pain, which mimics key clinical features of OA. Design: Effects of preventative vs therapeutic treatment with an anti-NGF antibody (monoclonal antibody 911: muMab 911 (10 mg/kg, s.c.)) on pain behaviour (weight bearing asymmetry and hindpaw withdrawal thresholds (PWT)), cartilage damage, synovitis and numbers of subchondral osteoclasts were investigated in the monosodium iodoacetate (MIA) model. Potential direct effects of NGF on receptor activator of nuclear factor kappa-B ligand (RANKL) mediated osteoclastogenesis were investigated in cultured human osteoclasts. Results: Intra-articular MIA injection resulted in significant pain behaviour, cartilage damage, synovitis and increased numbers of subchondral osteoclasts. Both preventative and therapeutic treatment with muMab 911 significantly prevented, or reversed, MIA-induced pain behaviour, but did not alter cartilage or synovial pathology quantified at the end of the treatment period. NGF did not facilitate RANKL driven osteoclast differentiation in vitro, but preventative or therapeutic muMab 911 reduced numbers of TRAP positive osteoclasts in the subchondral bone. Conclusions: We demonstrate that anti-NGF antibody treatment attenuates OA pain behaviour despite permitting cartilage damage and synovitis. Indirec
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