We develop a complete and consistent description for the hadron spectra from heavy ion collisions in terms of a few collective variables, in particular temperature, longitudinal and transverse flow. To achieve a meaningful comparison with presently available data, we also include the resonance decays into our picture. To disentangle the influences of transverse flow and resonance decays in the m T -spectra, we analyse in detail the shape of the m T -spectra.

We use ͑3ϩ1͒-dimensional hydrodynamics with exact longitudinal boost invariance to study the influence of collision centrality and initial energy density on the transverse flow pattern and the angular distributions of particles emitted near midrapidity in ultrarelativistic heavy-ion collisions. We concentrate on radial flow and the elliptic flow coefficient v 2 as functions of the impact parameter and collision energy. We demonstrate that the finally observed elliptic flow is established earlier in the collision than the observed radial flow and thus probes the equation of state at higher energy densities. We point out that a phase transition from hadronic matter to a color-deconfined quark-gluon plasma leads to nonmonotonic behavior in both beam energy and impact parameter dependences which, if observed, can be used to identify such a phase transition. Our calculations span collision energies from the Brookhaven AGS ͑Alternating Gradient Synchrotron͒ to beyond the LHC ͑Large Hadron Collider͒; the QGP phase transition signature is predicted between the lowest available SPS ͑CERN Super Proton Synchrotron͒ and the highest RHIC ͑Brookhaven Relativistic Heavy Ion Collider͒ energies. To optimize the chances for applicability of hydrodynamics we suggest studying the excitation function of flow anisotropies in central uranium-uranium collisions in the side-on-side collision geometry.

We study relativistic SϩAu collisions at 200A GeV/c using a hydrodynamical approach. We test various equations of state ͑EOS's͒, which are used to describe the strongly interacting matter at densities attainable in the CERN-SPS heavy ion experiments. For each EOS, suitable initial conditions can be determined to reproduce the experimental hadron spectra; this emphasizes the ambiguity between the initial conditions and the EOS in such an approach. Simultaneously, we calculate the resulting thermal photon and dielectron spectra, and compare with experiments. If one allows the excitation of resonance states with increasing temperature, the electromagnetic signals from scenarios with and without phase transition are very similar and are not resolvable within the current experimental resolution. Only EOS's with a few degrees of freedom up to very high temperatures can be ruled out presently. We deduce an upper bound of about 250 MeV for the initial temperature from the single photon spectra of WA80. With regard to the CERES dilepton data, none of the EOS's considered, in conjunction with the standard leading order dilepton rates, succeed in reproducing the observed excess of dileptons below the peak. Our work, however, suggests that an improved measurement of the photon and dilepton spectra has the potential to strongly constrain the EOS.