What are the best loudspeakers under $4000 to re-create lifelike piano

I think if Bosendorfer wanted to compete with Yamaha they'd make motorcycles. Irrelevant but true.

I actually purchased the LS50s based on piano reproduction. My budget was Eur 2000.
Previously I owned B&W685 and they were terrible in the upper piano registers (too forward and thin).
I tried B&W PM1 and I think piano sounded fantastic on them, but this is a bit of a laid back speaker and the treble is tilted upward. It lends nice air and stringy definition of the piano. very nice for my taste. But I eventually returned the pair because I felt them a bit too laid back and I felt that the first order crossover crossed too high is too specific sounding.
I settled on the LS50 with best blend of faithful piano reproduction and lack of coloration.

I know how live piano sounds, I attend many concerts and take my daugter to classes. Sha has played Steinway, Bossendorfer, Feurich, uprights, etc. It’s very hard to describe what real piano sounds because there are many variables, like the condition and design of the piano, the room, the listener’s position and finally and most important the recording.
Most of classical recordings are far field and the there is too much room contribution. Most of jazz an especially pop is close miked and it often sounds like we never really hear it in a room or concert hall when played unamplified.

I would wholeheartedly recommend LS50 for piano reproduction. (with or without a sub)
B&W PM1 for a more musical and airy reproduction.

@vahes

A well recorded, uncompressed, Steinway-D needs a fairly large, efficient, and expen$ive speaker to reproduce its full fire power at a realistic volume ...

Indeed, an important aspect here is sheer radiation area coupled with high efficiency to give way to the physicality and full dynamic range needed for the more authentic reproduction of a piano. Add to that coherency, relative timbral accuracy, not least (transient) speed/dynamic prowess, and a low degree of smearing through the whole of the (wide) frequency span - as rightly pointed out by poster @james_w514 into the sub-region as well, all of which is no small task.

Listening to a grand piano at a relatively close distance can be an extremely physical, dense and dynamically (and emotionally) startling experience, just as it can be a very liquid/floating and gentle instrument to take in. The trick is to incorporate the whole of the envelope of these traits mentioned into a speaker, the "gentleness" as well as the sheer force of the instrument, for it to be a more convincing reproduction - not something realistically attained with a <$4,000/pair speaker. This is not strictly what the OP is inquiring on, though; for that to be accommodated several other posters above have chimed in.

I'm not the "audiophile" everyone else here is, however I'm trying to upgrade my system to get to that level...I might get flamed here, however I bought a set go Bryston Mini T speakers and am floored by the neutral and wide spread spectrum they cover. (20Hz to 20Khz) they produce a very natural and clean sound.
From all I've read it does matter what's driving them but they are solid performers....And they are less than $4K new with a 20 yr warranty.

@inna
You really do surprise me by saying if it is digital forget it. I have heard some digital master recordings that if we had access to would dispel that myth straight away. The way I see it the recordnig process has a lot to do with it at the microphone end. We are by the way trying to record sometime levels of 110db. I have heard some valiant attempts to portray it but they were usually through very high end active speaker systems with massive active sub woofers also and in recording studios I used to frequent. Only then would I say we are getting towards it in any medium. In the 70s I used to burn out bass panels on my Quad 57s by trying to replicate what I had just heard from the concert hall previously ( not recommended as it used to cost a fortune with each visit to Quad). No I havn't heard proper portrayal from any domestic setup that I could say, yes that sounds like a full range piano recording that I am listening to. If you go to concert hall recitals with any regularity you soon get to know the sound the recording engineer is trying to capture as I say with good and not so good results.I remember years ago going to The Queen's hall in Edinburgh to hear Boris Beresovsky
play Mussorgsky's Pictures at an Exhibition. When It came to The Great Gate of Kiev at the end of the piece the younger females in the audience were cringeing and some were even holding their ears as we all know younger females have better hearing than most of us men.That was the first time that I knew what a Steinway Model D concert grand was actually capable of. As an aside The BBC were recording that concert that night and the later broadcast bore no relation to the experience in the hall.